The Hydromagnetic Stability of the Modified Plane Couette Flow in the Presence of a Transverse Magnetic Field

The hydromagnetic stability against small disturbances is investigated on the plane laminar motion of an electrically conducting fluid between parallel plates in relative motion in the presence of a transverse magnetic field. Curves of the neutral stability in the (α, R )-plane (α, the wave-number; R , the Reynolds number) are calculated for various values of the Hartmann number M . It is thus found that the critical Reynolds number R c is infinite for M <3.91 as well as for ordinary plane Couette flow. As M increases from 3.91, R c decreases rapidly to a minimum value of 3.8×10 5 when M =5.4 and then increases steadily to its asymptotic value, 50000 M , for sufficiently large values of M (>15). Thus, we may conclude that the flow is always stable for 0≦ M ≦3.91, destabilized by the magnetic field for 3.91< M <5.4 and stabilized reversely for M >5.4.